Lightsout - I haven't had Mr. Shufflin convert one of my M1's yet. Every time I decide which one to send him I end up finding another M1 locally that I just have to have, or I change my mind on caliber, stock choices, etc. However, based on a lot of reading here, and my understanding of what the various rifle grades from the CMP are, I'll give my opinion.
I think the answer depends on what you want the final result to look like in terms of metal, stock, throat erosion, and possibly muzzle wear. Any rifle you buy from CMP will safely function, and any rifle Mr. Shufflin converts for you is going to safely function. The higher the grade rifle you start with, the lower the variables that may matter to you present. These seem to be:
a. appearance and condition of the stock: a higher grade rifle should provide a better looking stock (or you can buy a new stock);
b. the condition of the metal (i.e., pits, etc.): the higher the grade, the better the condition the metal should be;
c. throat erosion: the higher the grade, the lower the TE may be;
d. condition of the rifling: the higher the grade the better you may receive (or buy a new barrel for installation);
e. stock to receiver fit: the higher the grade the better you may receive;
g. wear on the various parts of the rifle: the higher the grade the better you may receive;
h. perhaps others.
Some of these are aesthetic only, but the aesthetics are already going to be enhanced by re-parkerizing the receiver, barrel, sights, etc. Some of these effect accuracy somewhat, but the Mini G is is not designed or sold as a target rifle. Whatever the inherent accuracy of the rifle you buy, your resulting Mini G will likely be more accurate, simply by eliminating the forward 8" of the barrel, and thereby removing the highest wear area and creating a brand new crown.
When I finally decide which rifle to have converted, it will be a Service Grade, both because all I have are Service Grades or better, and because I want the best condition internals, no pitting in the metal, etc.I also have a new laminate stock to go with it, and it will get a new barrel.
Will my resulting Mini G shoot any better than a Rack Grade conversion? Does it need to shoot better? And if it does, how much better is that and am I a good enough off-hand shooter to tell the difference? I hope the answers to those questions are "yes", but in all likelihood, I doubt that when shooting off-hand I could group the rifle any better than a Rack Grade without new stock, barrel, etc. Nevertheless, I want the tightest fitting, best looking, etc. Mini G simply because . . . . well, simply because.
So, in the end I think it comes down to what you want it to look like, and how much more you want to spend to increase the aesthetics in your eyes, and/or possibly increase the accuracy of the finished product.
JGW